# Planar Theory

• 13 Replies
• 4889 Views #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Planar Theory
« on: October 28, 2017, 07:55:15 PM »
I have decided to do what Intikam and Sandokhan have been doing, having a space for notes, workings, descriptions, etc. regarding planar theory (flat earth). Will mostly do my accepted ideas and models but will also include other things I may come across. So, this will be like my personal input for flat earth.

Every now and then, I'll add stuff to this thread and have it build up.
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #1 on: October 28, 2017, 08:08:55 PM »
Satellites orbit a flat earth The lesson that I want you to take away from this is that, in a curved space (or spacetime!), straight doesnt mean what you think it means. In flat space, a geodesic is a straight line. But in curved space, a geodesic is not a straight line. But its the closest thing to a straight line you can get. Indeed, its the appropriate definition of straightness.

In curved spacetime, straight lines look curved.

- http://www.thephysicsmill.com/2015/08/15/general-relativity-is-the-curvature-of-spacetime/

So what happens when I stand on a cliff and drop a ball from the top of the cliff? The ball wants to take the straightest possible path through spacetime. Since I dont throw the ball, I just drop it, it starts in a path roughly like that of the blue arrow. This is a path of constant radius where the only motion is forward in time. It should be roughly visible in the picture that such a path is extremely bendy. The more the ball moves either towards or away from the Earth, the straighter the path.

Of course, because the ball cant travel faster than light. So a path like that of the red arrow, which is almost a straight line, isnt valid. The ball has to be within my light cone. Therefore, the worldline of the ball will be some path that travels both forward in time and towards the Earth. And because of the way space and time curve, this will appear as an accelerating path. I plot the geodesic for the ball in figure 9. Note that it approaches a straight line. Thats because as it accelerates its approaching the speed of light (we are neglecting air resistance and exaggerating the distance from the surface of the Earth to make that happen). Note also that the speed of light is a straight line thats wider than 45 degrees. Thats because of the stretched axis. The path of the ball is curvedit curves with the surface, after all. But its as straight as it possibly can be. And thats what makes it a geodesic.
http://www.thephysicsmill.com/2015/09/06/our-local-spacetime/

John Davis:
Consider a theoretical object in a perfectly stable orbit around a theoretical planet in a traditional round earth manner. Remember from Newtons laws of motion: an object in motion tends to stay in motion and in the direction it is in motion. We can certainly say that the object in orbit that it feels no experimentally verifiable difference in force or pseudo-force - which is equivalent to saying it is experimentally not accelerating (and thus not changing direction or speed.) Remember, Einstein disillusioned our naive view of space based on the equivalence principle.

Our sight would lead us to believe this might be foolish, but if space is curved (and Relativity relies on the assumption that it is) it would be silly to not question our visual representation of space since by all accounts it appears as if our observational (and theoretical) language is ill equipped to deal with description of it.

We should assume that it is indeed travelling in a straight line as its experimental evidence points us to. The issue is with our naive view of geometry and space. Likewise we take the view that it is indeed in motion and not still.

Lets interpret the ramifications of the statement: an object in orbit travels in a straight (and thus flat), line through space through further thought experiment. First, we can define our field of interest in that taking all such theoretical orbits of our planet and realize them rightly as flat, thus defining the bounding space of interest also to be flat. It follows, given any orbit of this planet to be flat, the planet itself is flat since it satisfies our definition of flatness.

Let us again venture into thought experiment: eject some pods towards the earth from one such of our imaginary satellites at regular intervals along our orbit such that they are in free fall. Again, we can assume these are straight lines extending below to a translatable location on the surface of the earth, its geolocation. We can say these lines are normal to the trajectory of the satellite and they are normal to the ground, thus making the lines parallel. Since the orbit is straight, and the orbit relates directly to the geographical locations it is above, we have come a long way to show the planet is also flat.

Now let us consider what acceleration means. Acceleration by its nature means either a change in speed or direction, which is to say a change in velocity. So when we look at the parabola formed by a ball in motion we can recognize that it is for the most part accelerating - it changes both direction and speed. Now, let us examine the path if we remove the influence of gravity from our model as well as unbound the start and end points to allow it to move freely.

If gravity was not forcing the object downwards, it would then be travelling a straight path, parallel perhaps to our imaginary satellite and in this case tangent to the apex of our balls climb.

We can see by comparison between a theoretical object in orbit and our ball at the apex of its climb that if not affected by gravity it would travel a straight line. By repeating this experiment again and again with lower apexes of our ball, various orientations, and so on we see the earth itself, not just the paths of satellites, is flat.

https://theflatearthsociety.org/home/index.php/blog/einsteins-relativity-proves-earth-flat

"In the spirit of general relativity we model the spacetime
geometry, i.e., the universe we live in (or at least the relevant
part for our model) using a pseudo-Riemannian metric tensor
g = gµνdxµdxν
on a four dimensional manifold M. The set {M, g} describes
the four-dimensional spacetime and local coordinates on M
are xµ , µ = 0, 1, 2, 3. We have an affine connection ∇, which
is fully defined by the Christoffel symbols ∇∂ν ∂µ = Γσµν∂σ .
On a pseudo-Riemannian manifold we can specialize ∇ to be
the Levi-Civita connection and we get Γσµν =(1/2)gσλ(∂νgµλ + ∂µgνλ − ∂λgµν).
Then, the geodesic equation that describes the motion of freely
falling particles reads d2xµ/ds2+ Γµνσ(x)dxν/ds dxσ/ds= 0
and gives as solution curves the geodesics xµ(s) of the
spacetime. The affine parameter s along such a geodesic
can be interpreted as proper time and is, thus, related
to the reading of a clock that is transported along the
geodesic. Now, we fix a certain (known) geodesic (Xµ(s)) =
(X0 (s), X1 (s), X2 (s), X3 (s)) and this curve will be called
the reference geodesic in the following. To consider a neighboring
geodesic xµ(s) in a given coordinate system we make the ansatz
xµ(s) = Xµ(s) + ηµ(s)
and define, thereupon, the deviation vector ηµ (s) that connects
both geodesics. We assume, as sketched in Fig. 1, the four
velocity of the reference geodesic and the deviation vector to
be always orthogonal to each other,
gµνηµ dXν/ds= 0 .
Inserting (16) into the geodesic equation (15) gives a second
order differential equation that is quadratic in the deviation
vector. When this deviation vector is assumed to be very
small, we can linearize with respect to the deviation vector
itself ηµ(s) and its derivative dηµ (s)/ds if we further assume
small relative velocities. Thus, we obtain the so called standard Jacobi equation
D2ηµ(s)/ds2= −Rµτ νσ(X) ην dXτ (s)/ds dXσ(s)/ds ,
where the covariant derivative D/ds and the curvature tensor components Rµτ νσ are given by
D ηµ(s)/ds=dηµ(s)/ds+ Γµνσ(X) ην dXσ/ds ,
Rµτ νσ(X) = ∂νΓµτσ − ∂τΓµνσ + ΓµνλΓλτσ − ΓµτλΓλνσ .
In (18) we can clearly see that the curvature of spacetime induces
a possible non-linear deviation between two neighboring
geodesics. We have seen in the Newtonian case before that
the same effect of non-linear deviation was caused by nonvanishing
second derivatives of the Newtonian gravitational
potential and we have, thus, an intuitive understanding of the
role of the curvature tensor; The Riemann curvature tensor
includes second derivatives of the metric as well. A somewhat
detailed discussion of the equation of geodesic deviation can
be found in standard textbooks on general relativity like 
and . It should be mentioned that if we do not linearize w.r.
to the relative velocity dη(s)/ds a generalized version of the
Jacobi equation is obtained, see, e.g., , , , .
"

- https://arxiv.org/pdf/1508.06457.pdf

Satellites travel in an inertial frame of reference, which does not accelerate. On a round earth, satellites constantly accelerate by a change in direction, equaling the curvature in fall rate. General Relativity provides the experimental evidence and theoretical applications of a inertial (straight and flat) orbit. https://theflatearthsociety.org/home/index.php/blog/einsteins-relativity-proves-earth-flat
https://www.theflatearthsociety.org/tiki/tiki-index.php?page=Davis+Model
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #2 on: October 28, 2017, 08:25:48 PM »
Tides and Tidal "Forces"

(Hint: Not the 'force of gravity' we tend to think of)

Now, what's the velocity vector of the clock at Q'? Well, think how we got it: first we parallel transported v over to Q along w. Then we parallel tranported the result over to Q', since the curve from Q to Q' is a geodesic, which means its velocity vector is parallel translated along itself.
Now for the big question! We want to know if the clock at Q' is moving away from the clock at P'. To answer this, we compare its velocity vector to the following vector: what we get by first parallel translating v along itself over to P', and then over to Q'. That's the velocity the clock at Q' would have it it were at rest relative to the clock at P'.

Note that when we do this, we are taking the vector v and parallel translating it two different ways from P to Q' and getting two slightly different answers... then we compare these answers. If the answers were the same, the second clock would remain at rest relative to the first. But in fact they are not, and the difference tells us how the second one begins accelerating away from the first.

Now remember how curvature works: the result of

dragging v from P to Q to Q'

minus the result of

dragging v from P to P' to Q'

is going to be

-R(w,v,v)

where R is the Riemann tensor. But this is just the same as

R(v,w,v)

since the Riemann tensor is defined so that it's skew-symmetric in the first two slots.

In short, the GEODESIC DEVIATION EQUATION says the following:

Two initially comoving particles in free fall will accelerate relative to one another in a manner determined by the curvature of space. Suppose the velocity of one particle is v, and the initial displacement from it to the second is small, so that it may be represented as a vector w. Then the acceleration A of the second relative to the first is given by R(v,w)v. Or if you like indices,

Aa = Rabcd vb wc vd

http://math.ucr.edu/home/baez/gr/geodesic.deviation.html

Geodesic Deviation, 4D space-time continuum (also can be referred to as an aether) is non-homogeneous and therefore directly affects the path of particles in a 3D space. Suppose how these lines are effected by warped spaces:  "So far we have concentrated on the motion of test particles in curved spacetime. But
matter tells space how to curve, so we need a machine to quantify that as well. Well
examine this by defining the stress-energy tensor and looking at its components, then doing
a couple of examples of what the stress-energy tensor is in a particular circumstance.
That machine is the stress-energy tensor, sometimes called the energy-momentum tensor.
It is a symmetric second-rank tensor written T, or in component form Tαβ. At a given
location, the meaning of the components is as follows. Consider an observer with fourvelocity uα. That observer will see a density of four-momentum (i.e., four-momentum per unit of three-dimensional volume), of dpα/dV = −Tαβuβ."

- https://www.astro.umd.edu/~miller/teaching/astr498/lecture11.pdf

"Curvature of spacetime can be measured when we observe the geodesics of two freefall test particles deviating relative to each other. We will derive this deviation equation below.
In terms of the coordinates and the curve parameter u, these geodesics are represented respectively as:  and . Small coordinate differences can always be thought of as vectors. Hence we can let  be the small vector joining points on the two geodesics having the same u value. That is http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/GeodesicDeviation.htm

Parallel lines remain parallel in flat homogeneous space (-time): But in non-homogeneous curved spaces, we have a deviation away from the norm to non-parallel positions, just like lines parallel at one point converge in non-euclidean geometry:  This gives the illusion of tides, but they aren't anything special other than water following their path of least resistance in relatively non-homogeneous space regions as geodesics.
« Last Edit: October 28, 2017, 08:29:26 PM by AltSpace »
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #3 on: October 28, 2017, 08:34:04 PM »
Now what is the angle of deflection as described mathematically with this phenomena and light?
The angle of deflection = 4GM/rc^2
Where G is the gravitational constant, M is the mass, r is the distance from the mass, and c is the speed of light in a vacuum.

According to a study done with telescopes observing radio waves bear the sun, the deflection of radio waves by the sun precisely, and it confirmed the general relativity prediction of bent space time to a high degree (within 0.03 %), here it is as published in the Astrophysical journal:
https://arxiv.org/abs/0904.3992
The solutions in Table 5, using different selections of data, are all consistent with GR
value of the parameter γ = 1. For the results in this paper, we have taken an average of
the four solutions to obtain γ = 0.9998 ± 0.0003. This result is a factor of three times more
measure the gravitational bending: 0.9996± 0.0017 (Lebach et al. 1995), and 1.0002±0.0010
(Robertson et al. 1991). Using the radio geodetic data base of thousands of observing sessions
between 1979 and 1999, Shapiro et al (2004) obtained γ = 0.9998 ± 0.0004, comparable in accuracy to the present results. The result from the measurements as the spacecraft Cassini passed by the sun in September 2002 is γ = 1.00002±0.00002 (Bertotti et al. 2003), and was discussed in §1.
Although expected departures from γ = 1 are likely to be a factor of 10 to 100 smaller
than the accuracy of this experiment, some possibilities are: (1) The long-range scalartensor
interaction in scalar-tensor theories of gravity (Will 1993), and Damour & Nordtvedt
(1993) predict a lower bound for the present value of γ at the level of 10−6 ∼ 10−7
; (2)
The long-range vector-tensor interaction in vector-tensor theories of gravity (Kosteleck´y
2004) may suggest a spontaneous violation of the Lorentz invariance and could modify the
value of γ (Bailey & Kosteleck´y 2006); (3) The more complicated nature of the gravitational
coupling between the curvature and stress-energy tensor of matter may lead to changes
of γ (Jaekel & Reynaud 2005); (4) The plausible existence of the effective gravitons mass
(Babak & Grishchuk 2003) that would avoid the van Dam-Veltmann-Zakharov discontinuity
(van Dam & Veltman 1970; Zakharov 1970) would also effect the value of γ.
There are several changes in the design of a similar VLBA experiment that should
improve the accuracy of γ by about a factor of two. First, by choosing a set of sources
that can be observed when the sun is further north6
, each days integration time can be
increased from 6 to 10 hours, and the sources will be on average at higher elevations than
those from the present experiment. We estimate that a more northern experiment will lower
the position rms by about 20%.
Secondly, we lost some sensitivity in the determination of γ by not observing on days
when the gravitational deflection was relatively large (egs October 3, 4, 12, 13). We found
that the most accurate results are obtained between solar distances of three to five degrees,
corresponding to about three days to seven days from the nearest approach of the sources
with the sun. Thus, the addition of the above four observing days in the 2005 experiment
would have decreased the position rms by 25%. Rμν= Ricci curvature tensor
R = scalar curvature, gμν is the metric tensor
Λ = cosmological constant
G = Newton's gravitational constant
c = speed of light in vacuum
Tμν = stressenergy tensor

In that situation, there is no force making the particles deviate from the straightest possible lines; the mere fact that the particles are moving on a sphere means that, even if they still move as straight as possible, their paths will converge.

Einstein's theory is exactly analogous to this. In Newton's theory, gravity makes particles leave their straight paths. In Einstein's theory of general relativity, gravity is a distortion of space-time. Particles still follow the straightest possible paths in that space-time. But because space-time is now distorted, even on those straightest paths, particles accelerate as if they were under the influence of what Newton called the gravitational force.

http://www.einstein-online.info/elementary/generalRT/GeomGravity

"Gravity is not a force. What is a force, anyway? Newton clarified for almost the first time in Science what a force is: First I will say it, then explain it: A force is something which makes the motion of a body deviate from uniform straightline motion.

Newton pointed out that bodies have a tendency, inertia, to continue in whatever direction they are already going, with whatever velocity they have at the moment. That means uniform, rectilineal motion: steady velocity, same direction. Newton actually knew this was what would be later called a geodesic, since « a straight line is the shortest distance between two points ».

Newton then went on to say that to overcome inertia, to overcome this tendency, requires a force: force is what makes a body depart from the geodesic it is (even momentarily) headed on (its direction and speed).

It was then Einstein (and partly Mach before him) who said this does not get to the essence of the question. For Einstein, any coordinate system had to be equally allowable, and in fact, space-time is curved (as already explained by other posters). A body or particle under the influence of gravity actually does travel in a geodesic....i.e., it does what a free particle does. I.e., it does what a particle not under the influence of any force does. So gravity is not a force.

Newton did not realise that space-time could be curved and that then the geodesics would not appear to our sight to be straight lines when projected into space alone. That ellipse you see in pictures of planetary orbits? It is not really there of course since the planet only reaches different points of the ellipse at different times...that ellipse is not what the planet really traverses in space-time, it is the projection of the path of the planet onto a slice of space, it is really only the shadow of the true path of the planet, and seems much more curved than the true path really is.

( ¡ The curvature of space-time in the neighbourhood of the earth is really very small ! The path of the earth in space-time would even appear to be nearly straight to an imaginary Euclidean observer who, in a flat five-dimensional space larger than ours, was looking down on us in our slightly curved four dimensional space-time embedded in their world. It's ctct, remember, so the curving around the ellipse gets distributed over an entire light-year, and appears to be nearly straight...and is straight when one takes into account the slight curvature of space-time.)

Since every particle under the influence of gravity alone moves in a geodesic, it does not experience any force that would make it depart from its inertia and make it depart from this geodesic. So gravity is not a force, but electric forces still do exist. They could overcome the inertia of a charged body and make it deviate from the geodesic it is headed on: change its speed and direction (when speed and direction are measured in curved space-time).

Einstein (and me too) did not want to change the definition of force in this new situation, since after all electric forces are known to exist and are still forces in GR. So the old notion of force still retains its usefulness for things other than gravity. To repeat: if a body is not moving in a geodesic in space-time, you go looking for a force that is overcoming its inertia....but since gravity and curvature of space-time do not make a body depart from a geodesic, neither of them is a force."

https://physics.stackexchange.com/questions/3009/how-exactly-does-curved-space-time-describe-the-force-of-gravity

Geodesics are consistent across a uniform accelerating surface, they can be described as forces in Euclidean Minkowski space-time since they would be deviating from a straight line but couldn't be in warped space-time geometry. The moons distortion interacts with the surface, the Moon's spatially flat surface directly connects to these tides.
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #4 on: October 28, 2017, 08:59:20 PM »
The 4D Kleinbottle Model

https://www.theflatearthsociety.org/forum/index.php?topic=72364.0

It would be possible to represent a spatially flat surface in 4D as a Kleinbottle, which could be seen as combined Mobius strips.
In this case, the Earth itself is a spatially without boundary and so is like a sphere, easiest to visualize a non-boundary geometry as non-euclidean in 3D, but is a 4D euclidean object.
Consider a flat disc, you walk across it and fall off the edge, this means the surface has a boundary. Now, consider a sphere, you walk across it and come back to the same spot, this means the surface has no boundary. A kleinbottle may represent a flat surface with no boundary. This is the case in four spatial dimensions, but we will only visualize it in three (2D representations of 3D from a screen, which is for representing 4D).
Imagine a 2D world, where you can only perceive in two dimensions. Now visualize this: A Mobius strip, which has one boundary.
Now imagine a 2D observer looking at it, or basically, imagine the Mobius strip in 2D, it could appear something like an 8, where lines intersect. However, thats only in your limited 2D view, in 3D, they dont intersect; they cross underneath and meet with only one boundary, which can only be represented in 3D, but it still represents a 2D manifold. And even more general, a kleinbottle intersecting itself: But remember the case of the Mobius strip appearing to intersect itself but really crossing underneath as one boundary geometry, its an illusion of our 3D perception. In fact, a surface with no boundary may be interpreted as a spheroid or convex in 3D, since that is a basic no boundary surface, but it's best just to say it would be visualized as a surface with no boundary.

Now, consider a Kleinbottle that represents a Mobius strip with no boundary. Any traversal will in fact meet itself since no boundary of any sort exists, but it is a 2D manifold, able to be represented in 4D Euclidean space.
It becomes apparent that the Kleinbottle is attached Mobius strips.

There is no information available as to whether any compact manifold which is equipped with an intrinsically consistent riemannian metric may be embedded in euclidean space so that this metric is induced on it by the metric of the euclidean space. The simplest manifold which seemed to be a possible counterexample is a flat Klein bottle. An example of a flat Klein bottle embedded in euclidean 4- space is given here. The manifold of this example intersects itself. The example is offered to remove the strongest contender from the list of possible counterexamples. The embedding equations of the Klein bottle are x\  cos v cos u1 #2 = cos v sin u, u u %z = 2 sin v cos  ; x4 = 2 sin v sin   2 2 The following identities are clearly satisfied : Xi(u, v + 2TT) = Xi(u, v), Xi(u + 2x, 2ir  v) = Xi(u, v). These are just the identifications of points which by definition of the Klein bottle convert the u, y-plane into a Klein bottle. The components of the metric tensor are £=1 , F = 0, G= l + 3 cos2 v, and these can be transformed into the more usual form 2=1 , 7 = 0, 5= 1 by an obvious transformation involving an elliptic function.
- http://www.ams.org/journals/bull/1941-47-06/S0002-9904-1941-07501-4/S0002-9904-1941-07501-4.pdf

A true Klein Bottle lives in 4-dimensions. But every tiny patch of the Klein Bottle is 2-dimensional. In this sense, a Klein Bottle is a 2-dimensional manifold which can only exist in 4-dimensions!
Alas, our universe has only 3 spatial dimensions, so even Acme's dedicated engineers can't make a true Klein Bottle.
A photograph of a stapler is a 2-dimensional immersion of a 3-dimensional stapler. The true stapler has been flattened into the flatland of the photo. In the same way, our glass Klein Bottles are 3-D immersions of the 4-D Klein Bottle. Acme's Klein Bottle is a 3-dimensional photograph of a "true" Klein Bottle.
A Klein Bottle cannot be embedded in 3 dimensions, but you can immerse it in 3-D. (An immersion may have self-intersections; Embeddings have no self-intersections. Neither an embedding nor an immersion has folds or cusps.)
We represent a Klein Bottle in glass by stretching the neck of a bottle through its side and joining its end to a hole in the base. Except at the side-connection (the nexus), this properly shows the shape of a 4-D Klein Bottle. And except at the nexus, any small patch follows the laws of 2-dimensional Euclidean geometry.
Contrast this with a corked bottle -- say, a wine bottle. It has two sides: inside and outside. You can't get from one to the other without drilling a hole or popping the top. Once uncorked, it has a lip which separates the inside from the outside. If you make the glass arbitrarily thin, that lip won't go away. It'll become more prominent. The lip divides one side of the bottle from the other. So an uncorked bottle is topologically the same as a disc ... it has two sides, separated by a boundary -- an edge.
But a Klein Bottle does not have an edge. It's boundary-free, and an ant can walk along the entire surface without ever crossing an edge. This is true of both theoretical Klein Bottles and our glass ones. And so, a Klein Bottle is one-sided.
A Klein Bottle has one hole. This, in turn, causes it to have one handle. The genus number of an object is the number of holes (well, it's more subtle than that, but I'm not allowed to tell you why). Other genus-1 objects include innertubes, bagels, wedding rings, and teacups. A wine bottle has no holes and so is genus 0. (The genus of a human being is difficult to define because it depends on what you consider a hole -- I'd estimate most people have a genus of 0 to 4, slightly higher when yawning. Pierce your ear and you'll increase your genus by one.)
As an alternative to buying an Acme Klein Bottle, you can save money by just memorizing this set of parametric equations, since it defines the surface of every Klein Bottle.:
x = cos(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))
y = sin(u)*(cos(u/2)*(sqrt_2+cos(v))+(sin(u/2)*sin(v)*cos(v)))
z = -1*sin(u/2)*(sqrt_2+cos(v))+cos(u/2)*sin(v)*cos(v)
or in polynomial form: There would be no 'edge' or cross section, it would be a one sided 4D Euclidean surface.
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #5 on: October 28, 2017, 09:04:01 PM »
The Non-Euclidean Relativity Model

The Relativity model is a flat earth model that states the Earth is a flat plane in non-euclidean aether (space-time continuum) in relative motion with other celestial bodies, including the sun, moon, planets, and stars. This is a combination of Einsteins General Relativity and The Ferrari Effect. This is one of the only flat earth models that dont rely on the conspiracy (weak or strong) and is unique in that it is based on Relativity (unlike many other typical flat earth models).

Link I recommend for some other explanation of it:  https://theflatearthsociety.org/home/index.php/blog/einsteins-relativity-proves-earth-flat

The Earth is a flat plane including the sun, moon, planets, and stars. The Earth is no more unique in terms of its physical geometry than the other celestial bodies. The universe consists of aether (basically space-time), which is bent around any large mass. Think of any mass as displacing the aether, a large mass will bend aether around it. All large masses will bend aether around them in a similar way, following that distortion of otherwise flat space. This means that the Earth bends aether around it, including the moon, sun, planets, and distant stars.
Aether is a term that represents the fabric of the 4-dimensional space-time continuum, in which times and distances between event pairs vary by the inertial frame of reference in which they are determined, while any event pair remains independent of the inertial frame of reference in which they are recorded. Aether can bend due to energy/mass, which is basically described in Einsteins field equations, basically put out as:
Gμν=8πTμν
Where Gμν is the Einstein Tensor (with the geometry of space-time), and Tμν is the stress-energy tensor, which describes the movement of matter and energy through aether.
Please note that this is how aether is defined into this specific flat earth model, and is not to be taken into the context of other models.
Now, it is important to define flat plane in this model because this model does fall under the category of being a flat earth model. Flat in this case, does not mean two-dimensional, anyone could agree that the existence of mountains is not something that defines the geometry of the Earth when we are talking flat or round Earth. Rather, it is something based on space and how it relates to the Earth. A flat plane would be defined by the ability to traverse it in a straight line between two spatial coordinates. A straight line would be a line in a constant direction in three dimensional space, or any tangent vector on the surface always touching across it would be a flat surface and therefore a flat earth. So, if the Earth is able to be traversed in a straight line parallel to the surface (constant distance from it in traversal), it follows under the definition of a flat plane. Due to the fact that space is bent around the Earth, a straight line traversing the Earth in bent space will appear to curve relative to an observer in flat space around it, while maintaining a straight line since space curves independent of this line. This means that it maintains itself as straight but in simplistic terms, space curves instead of the line. With this, we start jumping into Frames of reference, which is an important concept in relativity. A great analogy is an elevator in space accelerating in a direction at 9.81 m/s/s (accelerating by going 9.8 meters per second faster for every second that goes by), which is indistinguishable from standing on Earth.
We can deduce that in the Earths non-inertial reference frame, the bending of space makes travelling through it as if in a straight line through flat space, but the space distortion around it changes its direction from a frame of reference independent of this bent space, so, we can define the path of an object through this linear direction as straight, and therefore flat. Flat can also and accurately be defined as the straight path of an object according to Newton's first law, which would be considered a satellite. Such a path defined as parallel to a straight path through space defines the path as flat, and therefore the Earth as flat. If we were to leave the Earth and look back at it, it would indeed appear as a curved spheroid, this is because the aether bends around it and therefore it becomes apparent when you can see across it, but from this appearance, we certainly cant distinguish whether it is flat or literally round as we cannot perceive how space is being affected from your standpoint away from Earth (The Ferrari Effect). The same applies to the sun, moon, and planets, they are perceived as spheroids from our standpoint on Earth, but you couldnt leap to the conclusion that it is surrounded by flat space from visual appearance. Due to the fact that aether bends due to mass like objects displace mediums, the Earth is flat and so are other masses throughout the universe.

What about the movement of the celestial bodies like the sun, moon, and stars? Is it geocentric or heliocentric? Such a concept of Heliocentrism or Geocentrism is non-existent in our universe since all motion is relative to other frames, so rather than saying the Earth rotates around the sun or the sun rotates around the stationary earth, it is most accurate to describe it as the Earth and sun are in motion relative to the other. This is most accurately described as a relative acentric description; I will call it relacentric. Relacentric as a new term, must be defined, so I define it as follows:
The barycenter rotation point between two objects is relative to each objects frame of reference, having each of the frames of reference as valid centers.
This challenges the common assumption of absolute motion; people tend to speak of the solar system and moving objects in terms of objective motion and objectively stationary objects. With this, they may confine all motion in terms of the solar system since other motion is irrelevant and proclaim we live in a heliocentric system, however, in absolute terms, this is incorrect, and it is simply used as a model of our solar system to explain movements for simplification and explanation in terms of basic laws and theories.  A Frame of reference is an abstract coordinate system that has fixed physical reference points that locate and orient the coordinate system and measurements. We can use numerous reference frames for distinctive purposes, but there is no correct one, to say so is nonsense, since motion is not absolute. If you were to be in a universe with only you as the frame of reference and no other, then you wouldnt be able to derive your state of motion. From this, we conclude that the Earth is in motion relative to other distinct reference frames following geodesics in curved aether. There is no center of rotation in any solar system or absolute orbit motion but rather the reference frame we define that is in the frames in relative movements serves as its own distinct center in which to observe and measure.

The Pillars of this Model

This model has a few main supports that keep it standing; crippling any of the supports will damage it.
The Pillars:
1.   Theory of General Relativity
2.   Aether- 4D space-time continuum (not the luminiferous aether medium of the late 19th century, but rather a term for space-time, which is influenced by mass)
3.   The Ferrari Effect

The Ferrari Effect is something not so well known outside of the Flat Earth Society. The Ferrari Effect is basically the effect of viewing the Earth and it appearing round (spherical) due to curved space. The appearance is actually an illusion due to how we interpret space in our minds, when viewing space as curved, we cant distinguish it from a round Earth at a glance, just like the accelerating elevator and standing on Earth with the gravity to give it that acceleration. The Earths geometry following the curved space is what makes it flat, so we can essentially say that areas of high density in molecular clouds collapsing into stars is them flattening out.

I defined flat Earth as the Earth being able to traverse it in a three dimensional straight line. Just like the path of an object in accordance with Newton's first law at a specific velocity.
This, on earth, would be defined as drawing a straight line from the apex of a parabolic path of a ball, forming a tangent. If it could be demonstrated that Earth can be traversed between two spatial coordinates in a straight path across, it satisfies a flat Earth.
Now, how would we demonstrate this? We can determine the nature of space's relation to Earth.
In the early 20th century, Albert Einstein proposed his theory of general relativity where space is non Euclidean and is the equivalent of acceleration, which can be standing on Earth or an elevator accelerating at 9.81 m/s/s. This means acceleration would be indistinguishable from a gravitational field. Space curves and therefore affects the straight path of any object. If this is the case, and space bends around any object, as long as the acceleration across it is relatively constant like is the case on Earth. This is because the change in bend of space gives the acceleration and keeps things on Earth. So, from this, we can deduce that a straight line follows the bend if space, giving a flat Earth.

Now, from an outer observer, it appears as if a straight line is curved since it follows the bend in space, but the observer following the bend is following a straight line while space is bending their path relative to outer flat space.
This is the Ferrari Effect, brought up by philosopher and free thinker Leo Ferrari.

Has it been verified as an accurate model?
Yes, it has. By observing distant objects in the universe, the path of light, and the deflection of radio waves near large masses.
It has been experimentally verified and observed that the path of light through space deflects relative to us as predicted by the curvature of space-time.
Here's a link with basic description and sources: http://w.astro.berkeley.edu/~jcohn/lens.html
As you can see in the diagram presented, the straight path of light follows the curvature of space, space defines the path of an object and so a straight line in curved space implies flatness.
Now what is the angle of deflection as described mathematically with this phenomena and light?
The angle of deflection = 4GM/rc^2
Where G is the gravitational constant, M is the mass, r is the distance from the mass, and c is the speed of light in a vacuum.
According to a study done with telescopes observing radio waves bear the sun, the deflection of radio waves by the sun precisely, and it confirmed the general relativity prediction of bent space time to a high degree (within 0.03 %), here it is as published in the Astrophysical journal:https://arxiv.org/abs/0904.3992
This lensing effect has been observed with distant galaxies with long red shifts and the sun. Another identification published:https://arxiv.org/abs/1405.3661
This effect has been observed with solar eclipses and visible stars bear the sun, verifying the predictions of general relativity.www.google.com/amp/s/www.wired.com/2009/05/dayintech_0529/amp/
Also, time is affected too by this curvature, which makes it so atomic clocks on Earth run slightly slower than farther away from it, the Hafelle-Keating experiment confirmed this by  comparing clocks of planes flying east and west and a stationary clock on the Earth's surface and found an inconsistency. These clocks were cesium beam atomic clocks. Here's where you can obtain the published paper on it:http://science.sciencemag.org/content/177/4044/166
This is a confirmation of general relativity and lacks an explanation by Newtonian gravitation (Basic Round Earth explanation with Minkowski space to explain the Earth's geometry).

If as general relativity claims, acceleration on Earth (accelerating free fall) is the result of the bending of space-time, then the curve in time and space accelerates any object to it. Think of a stationary object moving through time even though it is stationary in three dimensional space. Time is curved and so its path is curved. This curve is like a parabola on a graph. So, this object accelerates towards the Earth. It does this across Earth almost consistently, this consistent curve in space-time has a straight line between spatial coordinates travel a straight path through space while appearing to travel a non-Euclidean path from an independent frame of reference.

The Ferrari Effect

The Ferrari Effect is the effect of visualizing a flat plane as being a spheroid due to the curvature of aether (space-time dimensions). This was a prediction made by the philosopher Leo Ferrari that is currently a major concept in the Davis Relativity Model. Despite common conceptions, the appearance of a spherical Earth is not what defined a flat vs round surface geometry. A flat earth is defined by its surface geometry being so that it is traversable in a straight line as defined by the direction of linear motion according to Newtons first law. With non-Euclidean space, a flat earth appears indistinguishable from a spheroid earth from an external point of view (just like acceleration and gravitation), what separates them is the geometry of space and its relation to Earths surface. Since space defines direction and geometry, the deformation of space relative to homogenous space has an equivalent definition of the geometry of a mass; it is just defined in relation to how space is changing or non-homogenous. This is based on general relativity and its conception of space.
The Ferrari Effect deals with the visual appearance of Earth, and its main implications include the possibility of orbit (considering the non-Euclidean nature of space), the potential accuracy space travel as presented by space agencies/NASA today, and an explanation of apparent curvature at high altitudes. The Ferrari Effect allows for the consistency between flat earth and modern space travel, since the apparent spheroid shape of the Earth from space travel footage and photos. Typical Flat Earth models and/or representations include the assumption that space travel is faked as a conspiracy, this is largely because of the inconsistency of the claims and apparent documentation of space travel and flat earth models and theories.

The Ferrari Effect was verified by observations and experimentation of space travel and curved aether.

Why it should be more considered in mainstream FE

As anyone with a fair understanding in Flat Earth 101 (the basics of flat earth views and models) knows, this specific model is very unique and significantly off of the mainstream. This model differs in numerous ways to the classical mainstream ones:
1.   There is no accurate map projection that conveys the surface, since space is non-Euclidean in this model and therefore cant be mapped on 2D to complete scale.
2.   There is no surrounding ice wall; this model is bi-polar (two poles, north and south), allowing north-south circumnavigation.
3.   There is no edge or surrounding worlds beyond; this model has the Earth contained in non-Euclidean space, so the curved space meets around it.
4.   The celestial bodies are not and need not be close to Earth, space curves away relative to the outer bodies surrounding straight across flat space.
5.   Outer space as conceived by modern society does exist, in contrast to the mainstream FE view that the celestial bodies are in a near, small, and confined space above us.
6.   Satellites, space travel, Apollo moon landings, astronauts, and modern space exploration are all consistent with this model, as opposed to the mainstream FE concept of The Conspiracy with the faking of space travel.
7.   This FE model is most consistent with modern mainstream science and with general relativity.
Why should planarists consider this? It appeals to skeptical globe earth advocates since it describes and works in terms of relativity. Any skeptic approaching flat earth will have many objections, questions, and potential ridiculing to go through. This will give the skeptic a reason to rethink how they originally thought this debate really means. Not only that, it is a model that can be held up to scrutiny, any flat earth model with that characteristic deserves to be considered. It also gets us to ask how we should draw the line between flat vs round earth. I consider this to be among the most advanced FE models today.
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #6 on: October 28, 2017, 09:07:59 PM »
FAQ

How do basic phenomena like day-night and seasons work in this model?

Day-night occurs by the sun moving relative to the Earth in a circle around it, and the curved aether gives it its apparent position and the sun sets to night when the sun is facing away from your position relative to the aether bend you are in. Seasons are the varying position of the sun relative to the Earth in a annual cycle, with its position directly perpendicular to the tropic of cancer in the June solstice, the equator at the equinox, and the tropic of Capricorn in the December solstice.

How does Gravity work?

Masses will follow the aether bend around and towards the Earths large mass; this gives acceleration and therefore makes an observer standing on Earth in a non-inertial reference frame. The warping of time and space gives all objects acceleration on earth; they simply follow a straight geodesic through this warped space-time. The bend in space and time will accelerate the path of any object to Earth. Think of this as the change in aether accelerating object paths through time and space into earth, giving the illusion of gravitation.

But isnt it true that the acceleration across Earth is not completely uniform and so its invalid to compare it to a uniformly accelerating elevator?

For the purposes in mind here with that scenario, this is not important and an irrelevant consideration, since the acceleration experienced by a single observer standing somewhere on Earth compared to an accelerating elevator is what we are imagining.

This model seems very similar to the round earth; why not just consider this as the round earth?

The definition of a flat earth fits whats described in this model; therefore it is a flat earth model, not round earth, so whatever striking similarities may exist in your conception of a spheroid earth to this are therefore irrelevant.

How far and large are the sun, moon, and stars in this model?

Same distances as the modern mainstream heliocentric model, approximately 93 million miles for the sun, 239,000 miles on average for the moon, and numerous light years for the stars. The sun would then be about 2,713,406 miles in diameter, the moon approximately 6,790 miles in diameter, and the stars will vary with many larger than the sun.

Wait, it seems you got the diameter and circumference mixed up, is that a mistake?

Im glad you noticed, I used the circumference as the diameter because Im thinking of them as flat bodies, by traversing them in a straight line, the diameter would be the same as we determine the circumference of them since we treat them as spheres as thats how they appear from our point of view. However, remember the Ferrari principle, it applies to the celestial bodies as well, they appear as if they are spheres but we are observing a bend in the aether, curved space.

So, the sun, moon, planets, and stars are flat too?

Yes, they all bend aether around them due to their mass, making them flat just like the earth.

How does the conspiracy fit here?

As far as I know, this is the only flat earth model that does not have the conspiracy as a necessary consequence. Satellites travel in a straight line according to Newtons first law while the curved space gives it the orbital path (its actually travelling a flat/straight line in curved space) and the supposed pictures of Earth from space and Apollo missions would fall under the Ferrari Effect, the curved space giving the appearance of a round earth. The Apollo Astronauts landed on a flat moon, since if they tried to cross it in a straight/flat line, they would traverse it entirely. However, since the moon has lower mass, the aether bend has a lower magnitude, and therefore lower acceleration on the moon.
Since all paths of objects on Earth follow straight geodesic paths through the aether, wouldnt that imply that Earth curves up, down, or give an undulating pattern in the case of elliptical orbits and therefore not be flat relative to numerous observers?
The definition of a flat earth provided here implies that the straight line geodesic be a parallel traversal to directly define the Earths surface itself. Such geodesic paths exist in curved space-time, and define a flat earth. Examples of other geodesics dont define Earth since they arent parallel (or basically equidistant across the traversal) or traverse earth at all. We can define it as flat since its surface is derived as a flat one from such a parallel geodesic.

In non-euclidean geometry, cant parallel lines be curved and flat and other odd things that may defeat this definition of flat?

In this case, we derive the Earth is flat because a line traversing the surface is in fact straight. The Earths surface itself is straight along with this parallel geodesic. This can be represented in a 2D plane and shown to be parallel and therefore the same, giving our flat surface.

Isnt the Relacentrism mentioned here without explanatory power since it doesnt include inertial forces and other defining factors for motion?

Explanatory power is simply what this can explain, and it explains all motion. All motion is relative between abstract frame coordinates and no inertial forces are required to explain this as such. Relacentrism is an explanation of motion mechanics in our universe according to the relativity model.

What are some other flat earth models that dont rely on the conspiracy?

There is also the 4D Kleinbottle model, which doesnt rely on a conspiracy since Earth is perceived as a sphere only because we can only perceive three spatial dimensions ourselves. Otherwise, there isnt very many, it is most typical that flat earth depends on the conspiracy under general circumstances.

Few specific variations:

What is terrestrial and planetary/stellar gravity?

Aether (4D space-time continuum) itself is warped by mass; this curves time and space as one, which accelerates any mass in its vicinity. Think of it this way, an object can move through 4 dimensions, three being spatial and the fourth temporal. The object moves through space, traversing a constructed area of coordinates in 3D space, and experiences time, so it is moving through time. If we have a stationary object, it still moves through time and therefore can be represented as changing 0 coordinates on the space axis, but changing position on the temporal axis, and if space-time itself is curved, time itself curves onto the space axis rather than being straight on the time axis and 0 in the space axis. So, the warp in time itself translates to movements in space, like a parabola, and so it accelerates through space by means of the interconnected 4D space and time. This produces the effect of Gravity, which also keeps objects in orbit by moving in straight lines through curved aether.

What does the Earth look like?

The warped aether field (gravitational field of Earth) gives Earth its Non-Euclidean aspect, so it indeed appears spherical and therefore cannot be depicted as a 2D map. Any 2D projection will be an approximation of Earths surface that cant match warped aether. This makes it a matter of preference of how I think Earth is best represented as a 2D map projection and the best I know of is this: https://wiki.tfes.org/images/thumb/c/c2/Altmap.png/400px-Altmap.png

How does the Sun orbit above the flat earth?

The sun and earth can both be described as moving relative to the other, with them both being inertial for the most part. There is no center of orbit since there are no privileged frames in curved aether. Heliocentrism and Geocentrism are simply constructed coordinate systems that presume an absolute motion to explain celestial motions and orbit. The suns position corresponds to different areas year round on Earth, with it being tilted in respect to the equator in both summer and winter and at the equator on the equinox.
"The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either coordinate system could be used with equal justification. The two sentences, 'the sun is at rest and the earth moves,' or 'the sun moves and the earth is at rest,' would simply mean two different conventions concerning two different coordinate systems." Major figures in cosmology, physics, and astronomy (Albert Einstein, Max Born, Stephen Hawking, George Ellis, and Fred Hoyle, among others) are in agreement that there is no scientific way to prove either model over the other, nor any non-philosophical/theological justification for doing so, SPECIFICALLY in the context of General Relativity.
-(Einstein and Infeld, The Evolution of Physics, p. 212 (248 in 1938 ed)
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #7 on: October 28, 2017, 09:31:44 PM »
Dual Earth

Dual Earth is a model by JRoweSkeptic (pseudonym) which states that the Earth is composed of two distinct hemiplane discs that form in low concentration of aether. Aether in this model is defined as a fabric of space in which all flow from high to low concentrations, all seeks to balance in equilibrium. In between the dual hemiplanes (within Earth), there is a very low aether concentration, so aether flows to that low concentration and so everything has a tendency towards the area of flow, which is gravity. The edge around the hemiplanes would be the equator, so crossing the equator results in traversing to the other hemiplane. Gravity varies depending on distance from the low pressure zone and therefore altitude. The fabric of space, aether, defines time and distance to traverse a particular area, with more aether in a particular area giving greater distance relative to the observer traversing it. With less aether, an observer traversing it covers less distance of a particular area. Aether defines, in fact, defines area and spatial coordinates because it is in fact space itself. With the lowest concentration of aether within Earth, walking from one hemiplane to the other is of no distance, it is simultaneous, as if they are connected directly. The sun, moon, planets, and stars are all rock and metal caught up in or near whirlpools directly across the two distinct hemiplanes, so there would be essentially two whirlpools in this model. These celestial bodies are heated by friction and to different degrees, depending on the location. The movement of celestial bodies is within aetheric whirlpools, which form by aether flowing to the inside of Earth and out the sides, which leaves a low pressure zone , it then forms a dome of aether to flow back to the inside of Earth. When it flows back from crossing above the hemiplane, it leaves a low pressure zone above, which has other aether rush to fill it in and this constant process creates a whirlpool pattern which continues as long as there is aether and the Earths low concentration. The stars are within this whirlpool, and so appear to circle above us, in the north and south hemiplane. The sun is inside the Earth and from geothermal energy and the Earths magnetic field. Its light and heat is in the low concentration inside the Earth which, by transmission of that Aether by flowing out to the whirlpool region above Earth, is visible as if it is above us and giving off heat, which is aetheric transmission.

Northern Hemiplane: Southern Hemiplane:  Championed by: JRoweSkeptic

Magnetic

In the Magnetic FE model, the Earth is a flat disc with a light and heat source shining through a polarization layer, which then follows the magnetic field lines of Earth, making the sun as we see it, a local source projection that is unique to every observers location, as they interpret the suns image through the magnetic field of Earth. The process by which the suns projections follows the magnetic field lines of Earth is of similarity to light passing through Ferrofluid under the influence of a magnetic field. The Earths magnetic field is like a torus field, similar geometry. Plotting the suns apparent path by azimuth and declination reveals this geometric pattern. The universe is essentially governed by magnetism under this model, which likely explains the movement of stars and planets and other astronomical phenomena as well. The magnetic torus field of Earth is not stationary but it actually moves by the increasing current in the field and then decreasing, which is the cosmic breath. This gives the effect of seasons, the sun (whatever it actually is) is seen as a source projection through this field that essentially oscillates by expanding and contracting, either from the North Pole or outside of Earth beyond the Antarctic. It then appears to be moving back and forth when it is really how the source is projected through an expanding and contracting magnetic field. It also may be likely that light on Earth may bend like with the Electromagnetic Accelerator theory, creating a horizon and specific field of view across the sky by means of magnetism and way light interacts with the layer and field above. The big thing with the model here is that it essentially describes a magnetic universe, a universe which is primarily governed by magnetism.    Championed by: Steve Torrence, Mike Cavanaugh, and Dr.Zack

Video here:

Bi-polar

This model is based on an approximate map projection with two poles, a north and South Pole. There is the North Pole and the Arctic, and Antarctica as a distinct continent and the South Pole. The sun circles each of these poles by season, shifting sides. There are two barycenter rotation points, above the north and South Pole. These are like celestial gears, and the sun shifts gears at the equinoxes, following the rotation of the stars. This forms an annual 8 pattern. The rotation of the stars above the two distinct poles is able to work out the Coriolis Effect and Foucault pendulum by etheric currents and/or celestial gravitation. The celestial gears meet at the equator. The celestial gears are etheric whirlpools that rotate the celestial bodies. The light from the celestial bodies, especially the sun, follows the currents of ether and therefore comes from varying angles to appear directly east or west when it is directionally northeast or northwest. Day night cycle works in accordance with the increasing refraction of the ether in which the light bends relative to the observer and reflects at higher altitudes, creating day-night spots. The sun rises and sets due to perspective and etheric light refraction. Light propagates through this ether and any movement of ether changes its position.
Circumnavigation may result in two ways, circling the North Pole, or the South Pole. The magnetic field of Earth in the Bi-polar projection is like a bar magnetic, where compass circumnavigation follows the magnetic field lines and therefore circles the Earth. The Earth is surrounded by an ice wall of some sort in this model and Antarctica and the Arctic exist because the rays of the sun mostly dont reach it enough to keep it from the low temps it has. So, the ice wall and Antarctica are distinct on this map. Aether whirlpool drag: Typical conception of refraction: Championed by: Tom Bishop

Neo-Classical

The Neo-Classical model is the mainstream original of the modern Flat Earth Society. It is a combination of the work of Albert Einstein (special relativity) and Samuel Birley Rowbotham (aka Parallax, flat earth). It basically proposes the Earth as a finite disk that is accelerating upwards at approximately 9.8 m/s^2. This would be the theory of Universal Acceleration. It also bases itself on special relativity, the laws of physics being the same in every inertial reference frame and the speed of light having the same value in every inertial reference frame. The acceleration of Earth is caused by the universal accelerator. It is unknown in this model what this universal accelerator is, but it is usually labeled as dark energy or aether that likely is accelerating from a past singularity. The universal accelerator accelerates anything it touches. This model is associated with the North Pole azimuthal equidistant map with a finite distance past the Antarctic ice. The atmoplane is kept in by a barrier, either a dark energy field in association with the magnetic field of Earth or a large surrounding ice barrier. The celestial bodies circle above the North Pole barycenter point or near it. The magnetic field of Earth works like a radial magnet. Magma is under the Earth and is maintained under enormous pressure due to acceleration. The acceleration of Earth pushing against us and changing our state of motion gives us and other objects weight, which happens because of the inertia of a mass. Zero-G would be a state of free fall, or basically the absence of influence of the upward acceleration. According to this model, the celestial bodies rotating above us may stay a relatively constant altitude without falling to Earth due to the acceleration wrapping above Earth and accelerating them at the same rate as Earth.
The Neo-Classical Model relies on five postulates
1.   The earth is finite disk.
2.   The earth is being accelerated upwards at approximately 9.80665 m/s2.
3.   The earth is the only known "disk" in the universe.
4.   The laws of physics are the same in every inertial reference frame.
5.   The speed of light, measured in any inertial reference frame, always has the same value, c.
- https://wiki.tfes.org/Neo-Classical_Model  Championed by: The Flat Earth Society

FE Theories:
1.   Universal Acceleration
2.   Aether
3.   Aetheric Whirlpool
4.   Antarctica Continent
5.   Antarctica Ice Rim
6.   Electromagnetic Accelerator
7.   The conspiracy
8.   Ice Wall
9.   Convergence Perspective
10.   Atmospheric Haze
11.   Denspressure
12.   Celestial Gravitation
13.   Celestial Gears
14.   Whirlpools
15.   Moonshrimp
16.   Firmament Dome
17.   Infinite Plane Gravitation (Newtonian Gravitation)
19.   Semi-transparent moon
20.   Aurora Electron
« Last Edit: October 28, 2017, 09:37:04 PM by AltSpace »
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #8 on: October 28, 2017, 09:43:53 PM »
Newtonian Gravitation on an infinite plane

Basic info: https://theflatearthsociety.org/home/index.php/blog/infinite-flat-earth-mathematics
https://www.theflatearthsociety.org/tiki/tiki-index.php?page=Infinite+Flat+Earth
https://www.docdroid.net/abhC8KU/infplane.pdf.html

Newtonian Gravitation is possible on an infinite plane of mass.
We can start with two postulates, an infinite plane of mass and Newton's formulas of Gravitational attraction:
F=G mM/r^2
F=mg
So, the force of gravitation is proportional to the product of masses and the Gravitational constant and inversely proportional to the square of the distance between their centers, and the force of gravitational is the product of the mass and gravitational pull or acceleration in Newtons.

Gauss's law, which is usually for electromagnetism, can show that with gravity, an infinite plane boils down to ∮gn dA = -4πGm. ∮ is a surface integral that represents infinite small surfaces covering the plane. n is a unit vector that is perpendicular to the surface, which represents up, and g is the gravitational pull, which represents down. Each point on the plane counterbalances with the other, making it stable.
The product of gravitational pull and unit vector n represents:
gn = -g
This leaves:
-g∮dA = g2A
and this leaves:
-g 2A = -4πGm
Given that mass is equal to the product of density and area, this simplifies to:

g = 2πG p

g is the gravitational pull, G is the gravitational constant, and p is the density of the plane.

Given this, we can determine the depth of the plane by noting  m = (density * Area * depth)
we get g = 2πG p d
where d is the depth.
If you plug in the values with  5.51 g/cm³, the estimated density of the Earth, you get 4,195.43 kilometers.
The gravitational constant doesn't have an exact measurement, but 6.754×10−11 m3 kg−1 s−2 works for this as an approximation.

Summary:  Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #9 on: October 28, 2017, 10:00:04 PM »
Electromagnetic Accelerator Theory
Light rays bend to the electromagnetic firmament, which creates a horizon. This is due to the magnetic field of Earth, light passes through a layer, the electromagnetic firmament and torus field accelerates the light and so it's position forms a parabola in x y co-ordinates. When it bends away from the Earth's surface, objects in its blind spot will appear to be obscured by a horizon.
The vertical distance of the ray is much larger than horizontal, so it's accuracy improves the closer it is to the vertical. The equation is represented as: y,x are the co-ordinates of the plane of the light ray.
c is the speed of light in a vacuum
β is the Bishop Constant, which is the magnitude of acceleration on a horizontal light ray.

Basic info: https://wiki.tfes.org/Electromagnetic_Accelerator
Founder and specialist of the theory: Parsifal

The decreasing dark energy potential is simply a placeholder term as we don't have knowledge of it's nature or complete behavior. It is also used in modern mainstream physics models.
This may have been experimentally observed.

http://www.rolf-keppler.de/lichtkrumm.htm
http://www.wildheretic.com/bendy-light-the-evidence/#Theodolites

In Riedern A.S. in Klettgau on May 24 2001 between 11 and 12am, the engineer Wilhelm Martin (deceased since 2009) conducted on experiment (which was witnessed by Rolf Keppler) with a theodolite (leveling device) called a dumpy level.
Two measuring poles were placed 1000m from each other. The dumpy level was placed in the middle of these two poles at the 500m distance. The built-in plumb line (spirit level) was then used to make sure the device was absolutely level to within 1 arc second, which is an accuracy of 0.5cm to 1km. Wilhelm then looked through the telescope and with the cross-hairs marked the zero mark on the measuring pole. He then turned the dumpy level around 180° and did the same for the other pole. These marks are now used as a control for the future measurements. Wilhelm then positioned the dumpy level 4m from the left measuring pole and adjusted the height of the theodolite so that it was level with the zero mark made previously when the dumpy level was located in the middle of the two poles. The dumpy level was then turned 180° and the cross hairs on the theolite were used to find its position on the right measuring pole 996m away. This was 12 to 14cm higher than the zero mark in the control. The exact same procedure as no.2 above was carried out, but this time moving the dumpy level 4m from the right pole, sighting the zero mark, rotating the level 180° and sighting the position on the left pole 996m away. The result was nearly the same as the other pole with a deviation of over 14cm higher than the zero mark.
This experiment was then repeated for different times of the day, on sometimes different days in the year, at the same location with varied results between 0 and 18cm higher than the zero mark. These results are listed below:

24.5.2001, 11am-12pm No.2 from 12 to 14cm, no.3 over 14cm higher 07.04.2001, 6pm Both no.2 and no.3 about 16cm higher 07.05.2001, midnight to 2am No.2 8cm higher, no.3 0cm (no difference) 07.05.2001, 8-9am No.2 8cm, no.3 12cm higher 05.7.2001, 5-6pm No.2 16cm, no.3 18cm higher

So at 996m we have readings from 0-18cm above the zero location, which was the mark measured at 500m. This difference therefore is over the extra 496m. According to Mr. Martin, this is a well-known phenomenon within the surveying community as surveyors always measure from the center if possible. The manufacturers also know about this as modern and expensive dumpy levels have built-in switches to compensate for this error in order to keep all readings the same as if light traveled in a straight line.

The overall actual physical height difference between the two measuring poles was only somewhere between 12 to 20cm, which eliminates refraction as a reason since the variation of air density over a few centimeters is non-existent. This leaves us with the only possibility left which is that light bends; but in which direction?

This is impossible on a round earth, as light must travel straight or down, but it does demonstrate a
useful implication of the horizon and celestial perspective on a flat plane. We interpret light in straight lines, which means it accelerating has our sight pointing up to the sky, and so objects can easily be past that blind spot and appear to descend into it at a horizon.
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### sandokhan

• Flat Earth Sultan
• Flat Earth Scientist
• 6747 ##### Re: Planar Theory
« Reply #10 on: October 28, 2017, 10:31:26 PM »
Satellites orbit a flat earth

They cannot orbit a flat earth using relativity theory.

https://www.theflatearthsociety.org/forum/index.php?topic=30499.msg1846706#msg1846706

http://file.scirp.org/pdf/JMP20120800006_80885197.pdf (pg. 718-720, 744)

Another observation that also clearly conflicts with the
constancy and isotropy of the velocity of light was discovered
during the implementation and calibration of
set-ups for Very Long Baseline Interferometry (VLBI)
radio astronomy observations. The resolution of optical
and radio astronomy observations can be improved by
orders of magnitude by analyzing the data recorded in
different observatories over the earth surface using interferometric
methods. The condition is that these data be
synchronous. The method consists in superposing coherently
the data recorded in different observatories with the
help of computers taking into account the instantaneous
position of the antennas etc. For the (VLBI) radio astronomy
observations clock synchronization at intercontinental
distances via the GPS achieve 0.1 ns. Nevertheless,
on testing the so synchronized clocks by confronting
them with the arrival of the wave fronts from distant
pulsars, which according to the TR may be synchronous,
it was observed that the pulsar signal reaches the foregoing
side of Earth 4.2 μs before the rear side along the
orbital motion of Earth. This discrepancy exceeds
the time resolution by more than four orders of magnitude.
Nevertheless along the transverse direction the arrival
of the pulsar signal was synchronous. This apparent
discrepancy in the GPS clock synchronization is again
raising very hot debates about the nature of space. Some
people speak of scandalous clocks that are biased
along the Earths orbital motion, others see in these
facts definitive prove that the velocity of light along different
directions within the solar system is not the same.

Many people believe that GR accounts for all the observed
effects caused by gravitational fields. However, in
reality GR is unable to explain an increasing number of
clear observational facts, several of them discovered recently
with the help of the GPS. For instance, GR
predicts the gravitational time dilation and the slowing of
the rate of clocks by the gravitational potential of Earth,
of the Sun, of the galaxy etc. Due to the gravitational
time dilation of the solar gravitational potential, clocks in
the GPS satellites having their orbital plane nearly parallel
to the Earth-Sun axis should undergo a 12 hour period
harmonic variation in their rate so that the difference
between the delay accumulated along the half of the orbit
closest to the Sun amounts up to about 24 ns in the time
display, which would be recovered along the half of the
orbit farthest from the Sun. Such an oscillation exceeds
the resolution of the measurements by more than two
orders of magnitude and, if present, would be very easily
observed. Nevertheless, contradicting the predictions of
GR, no sign of such oscillation is observed. This is the
well known and so long unsolved non-midnight problem.

In fact observations show that the rate of the
atomic clocks on Earth and in the 24 GPS satellites is
ruled by only and exclusively the Earths gravitational
field and that effects of the solar gravitational potential
are completely absent. Surprisingly and happily the GPS
works better than expected from the TR.

Obviously the gravitational
slowing of the atomic clocks on Earth cannot be due to
relative velocity because these clocks rest with respect to
the laboratory observer. What is immediately disturbing
here is that two completely distinct physical causes produce
identical effects, which by it alone is highly suspicious.
GR gives only a geometrical interpretation to the
gravitational time dilation. However, if motions cause
time dilation, why then does the orbital motion of Earth
suppress the time dilation caused by the solar gravitational
potential on the earthbased and GPS clocks? Absurdly
in one case motion causes time dilation and in the
other case it suppresses it. This contradiction lets evident
that what causes the gravitational time dilation is not the
gravitational potential and that moreover this time dilation
cannot be caused by a scalar quantity.
If the time dilation
shown by the atomic clocks within the earthbased
laboratories is not due to the gravitational potential and
cannot be due to relative velocity too then it is necessarily
due to some other cause. This impasse once more
puts in check the central idea of the TR, according to
which the relative velocity with respect to the observer is
the physical parameter that rules the effects of motions.
The above facts show that the parameter that rules the
effects of motions is not relative velocity but a velocity
of a more fundamental nature.

On the other hand, the time dilation effect of the solar
gravitational field on the atomic clocks orbiting with
Earth round the Sun, which is predicted by GR but not
observed, is a highly precise observation. It exceeds by
orders of magnitude the experimental precision and
hence is infinitely more reliable. If the orbital motion of
Earth round the Sun suppresses the time dilation due to
the solar gravitational field and moreover does not show
the predicted relativistic time dilation due to this orbital
motion, then it seems reasonable that a clock in a satellite
orbiting round the Earth in a direct equatorial orbit or in a
jet flying round the Earth too should give no evidence of
such a relativistic time dilation. The relativistic time dilation
alleged in both these round the world Sagnac experiments
is in clear and frontal contradiction with the
absence of such a relativistic time dilation effect in the
case of the orbiting Earth round the Sun.

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

N. Tesla

RUDERFER EXPERIMENT

Ruderfer, Martin (1960) First-Order Ether Drift
Physical Review Letters, Vol. 5, No. 3, Sept. 1, pp
191-192

Ruderfer, Martin (1961) ErrataFirst-Order Ether
Drift Experiment Using the Mössbauer Radiation,
Physical Review Letters, Vol. 7, No. 9, Nov. 1, p 361

in 1961, M. Ruderfer proved mathematically and experimentally, using the spinning Mossbauer effect, the FIRST NULL RESULT in ether drift theory.

"What students are not told is that the Turner & Hill experiment is a garbled version of a 1960 investigation by Ruderfer, who was seeking to discover fluctuations in gamma ray frequency which might indicate motion of an electromagnetic medium across the plane of the spinning disk, causing cyclic Doppler-type changes in the transit times of the gamma rays crossing that disk. Initially Ruderfer put it out that his results were negative for ether drift, but 14 months later he published an errata which stated that mathematical analysis had shown that if an ether wind were blowing across the plane of the spinning disk, one would expect that Doppler fluctuations in the frequency of the gamma radiation detected at the centre of the disk would be compensated by equal and opposite fluctuations in the emitted frequency of the gamma rays, caused by the effect of variations in the ether speed of the source.

What Ruderfer's experiment had stumbled on was that there could be a static electromagnetic medium at rest with respect to the rest of the universe. And it could be that any motion with respect to that medium affects the gamma ray source, and the central Mossbauer detector, by slowing down the rate of process of each by half the square of the ratio of each one's absolute ether speed to the absolute speed of propagation of light. If such were the case, it would follow (as a mathematical necessity) that irrespective of the direction and speed of ether drift of the lab, the central detector of the spinning disk would always observe a steady slowing of the gamma radiation frequency by half the square of the ratio of the spin speed of the source to the out-and-return speed of light, as measured by the detector in a reference frame which is non-rotating with respect to the fixed stars.

Ruderfer's experiment and his errata were of great significance in the history of modern physics because of their psychological impact on the ether deniers. Previously, the Michelson & Morley ether drift experiment had been successfully portrayed as 'negative' rather than 'null' because the proposed compensating factor, Fitzgerald contraction, was a theoretical construct. However, in the case of the Ruderfer experiment, the ether deniers were shocked to find that the experiment provided proof of the existence of the compensating factor in the observed frequency reduction, making it indubitably a null ether drift experiment.

Since the motion-induced frequency reduction of the gamma ray source is by a steady 'half the square of the ratio of the disk spin speed to the speed of propagation of the gamma rays', and since this is exactly the amount required to give the same result, irrespective of whether the disk is at ether rest, or is orientated edgewise (or at right angles) to a hypothetical ether drift, this constituted prima facie evidence for something for which the ether deniers have a particular fear and loathing - 'laws of nature which conspire to conceal the effect of ether drift'."

https://web.archive.org/web/20070315063351/http://egtphysics.net/Index.htm (select the Ether Drift article option)

http://www.tuks.nl/pdf/Reference_Material/Ronald_Hatch/Hatch-Clock_Behavior_and_theSearch_for_an_Underlying_Mechanism_for_Relativistic_Phenomena_2002.pdf

Analysis of the spinning Mossbauer experiments is a natural step toward analysis of the
slightly more complex and much larger-scale Global Positioning System (GPS). This
system constitutes a large scale near-equivalent to the spinning Mossbauer experiments.
The transit time between the satellite and ground-based receivers is routinely measured.
In addition, the atomic clocks on the satellite are carefully monitored; and high precision
corrections are provided as part of the information transmitted from the satellites.
Because the satellites and the receivers rotate at different rates (unlike the Mossbauer
experiments), a correction for the motion of the receiver during the transit time is
required. This correction is generally referred to as a Sagnac correction, since it adjusts
for anisotropy of the speed of light as far as the receiver is concerned. Why is there no
requirement for a Sagnac correction due to the earths orbital motion? Like the transit
time in the spinning Mossbauer experiments, any such effect would be completely
canceled by the orbital-velocity effect on the satellite clocks.

Specifically, there is substantial independent experimental evidence that clock speed always affects the clock frequency and, as the GPS system shows, the spin velocity of the earth clearly affects the clock rate. This being the case, the null result of the rotating Mössbauer experiments actually implies that an ether drift must exist or else the clock effect would not be canceled and a null result would not be present.

A GPS satellite orbiting the Earth, while at the same time the entire system is orbiting the Sun, IS A LARGE SCALE SPINNING MOSSBAUER EXPERIMENT.

Given the very fact that these GPS satellites DO NOT record the orbital Sagnac effect, means that THE HYPOTHESES OF THE RUDERFER EXPERIMENT ARE FULFILLED.

Why is there no requirement for a Sagnac correction due to the earths orbital motion? Like the transit time in the spinning Mossbauer experiments, any such effect would be completely canceled by the orbital-velocity effect on the satellite clocks.

However, indirectly, the counteracting effects of the transit time and clock slowing induced biases indicate that an ether drift is present. This is because there is independent evidence that clocks are slowed as a result of their speed. Thus, ether drift must exist or else the clock slowing effect would be observed.

In fact, there is other evidence that the wave-front bending and absence of the
Sagnac effect in the earth-centered frame is due to the clock-biasing effects of velocity
and that an ether drift velocity actually exists in the earth-centered frame. First, the
gradient of the solar gravitational effects upon clocks on the surface of the earth is such
that the clocks will speed up and slow down in precisely the correct way to retain the
appropriate up-wind and down-wind clock biases. Thus, the clocks must be biased or
else the solar gravitational effects would become apparent. #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #11 on: October 28, 2017, 10:46:52 PM »
They cannot orbit a flat earth using relativity theory.
Thanks for your info, but I don't quite see the relevance to that post in particular other than criticizing GR.

By the way, I was looking into your theory, and am wondering where I can find more info on it other than what I got:
https://forum.tfes.org/index.php?topic=4429.0

https://www.theflatearthsociety.org/forum/index.php?topic=30499.0

Is that mainly it?
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #12 on: October 29, 2017, 10:54:32 PM »
Eratosthenes and the Flat Earth

It is a common misconception that the measurements made by Eratosthenes prove a round earth, but rather show the divergence of rays from the sun.

We can use Eratosthenes' shadow experiment to determine the diameter of the Flat Earth.

Syene and Alexandria are two North-South points with a distance of 500 nautical miles. Eratosthenes discovered through the shadow experiment that while the sun was exactly overhead of one city, it was 7°12' south of zenith at the other city.

By sheer math, 7°12' makes a sweep of 1/25th of the FE's total longitude from 90°N to 90°S (radius).

Therefore we can take the distance of 500 nautical miles, multiply by 25, and find that the radius of the Flat Earth is about 12,250 nautical miles. Doubling that figure for the diameter we get a figure of 25,000 miles.

The earth is physically much larger, of course. A circle with a diameter of 25,000 nautical miles across is simply the area of land which the light of the sun affects, and represents the area of our known world.

-- https://theflatearthsociety.org/tiki/tiki-index.php?page=Eratosthenes+on+Diameter  And with the distance to the sun, it is possible to detect it by tracing the rays back to an origin. It becomes relatively simple to determine this,

h(tan02 - tan01) = b

So, all we need to know is the distance between two sticks and the angles they make with the light rays.
Info here: http://www.millersville.edu/physics/experiments/058/index.php
https://theflatearthsociety.org/tiki/tiki-index.php?page=Eratosthenes+on+Distance+of+the+Sun

A more simple way of looking at it is imagining on the equinox, where the sun's rays are perpendicular to the ground at the equator, and you determine the distance from the equator south and north which get the sun's light to strike the ground at a 45 degree angle, that distance from the equator would be the height of the sun above earth. This is because that forms an isosceles right triangle with the 45 degree angle and so has the height equal the distance from the equator.

However, another good point has come up:

When light refracts when passing through a magnifying glass, the shadows get longer, because the beams diverge further by refraction. This means that when tracing the light to a source, it is most accurate to trace it to the refractive layer, and so tracing it to the light source would be inaccurate. Your results will be below the actual light source above the refractive layer. This changes things a lot, and explains why Eratosthenes assumed we lived on a Sphere rather than a flat plane.
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein #### AltSpace

• Flat Earth Believer
• 411
• Neo-Planarist ##### Re: Planar Theory
« Reply #13 on: November 17, 2017, 10:08:19 PM »
John Davis on moon effects:

There are plenty of threads where I have provided citations and studies supporting this view. More than this, it is a fact known by educated men since antiquity.

Here are some commonly known facts that show the moons effect:
The mouse Acomys cahirinus notes a considerable drop in body temperature and activity during the full moon.
Bats tend to reduce their hunting to avoid the harmful polarized light of the moon.
Lions take advantage of the weakness of other animals during the full moon period by increasing their hunting rates.
Human doctor visits increase during the full moon.
Pet Vet visits increase during the full moon.
Corals go into a mating frenzy due to the lack of smaller biological enemies subdued by the full moon.
Some scorpians glow blue in the moonlight due to it attacking certain proteins.
Humans sleep worse in the full moon.
Doodlebugs - dig larger holes to trap prey during full moons showing increased predatory nature
Bats - (vampire bat) decrease their night activity during the full moon to avoid increased predators
Nightjars - increase predator nature during dark nights.
Spincy Mice - the full-moon affects their body temperature.
Primates that are attacked by aye aye are less active during the night and will shift their day schedule to avoid the full moon.

Now to a few studies and references:
Notes on the Folk-lore of the North-east of Scottland "Chapter XXI: Fish hung in moonlight poisonous, Sleeping in moonlight dangerous" "Mairt" killed when the moon increasing"

The most notable evidence, IMO, is that Lyme Disease symptoms become worsened during a full moon. Again you can google this yourself. The reproductive cycle of Borrelia burgdorferi is about 28-30 days - synced up with the full moon every 29.53 days.

Christian Cajochen, Songül Altanay-Ekici, Mirjam Münch, Sylvia Frey, Vera Knoblauch, Anna Wirz-Justice. Evidence that the Lunar Cycle Influences Human Sleep. Current Biology, 2013; DOI: 10.1016/j.cub.2013.06.029

Quote
Professor Piazza Smyth, the Astronomer Royal for Scotland, in his interesting account of a recent scientific expedition made by him to the Peak of Teneriffe, has set at rest the vexed question of the heat of the moonlight. He Bays that his thermometrical instruments were sensibly affected by the moon's rays, even at the lowest of two stations occupied by him at different elevations. In tropical climates meat which is exposed to the moonlight rapidly becomes putrid ; and in the Indies, the negroes who will lie sweltering and unoovered[sic] beneath the full glare of a tropical sun, carefully muffle their heads and faces when exposed to the moonbeams, which they believe will cause swelling and distortion of the features, and sometimes even blindness.
https://www.scientificamerican.com/article/the-effects-of-moonlight/

Quote
Data on five aggressive and/or violent human behaviors were examined by computer to determine whether a relationship exists between the lunar syndoic cycle and human aggression. Homicides, suicides, fatal traffic accidents, aggravated assaults and psychiatric emergency room visits occurring in Dade County, Florida all show lunar periodicities.
https://www.ncbi.nlm.nih.gov/pubmed/641019?dopt=Abstract

Quote
Data on homicides were analyzed by computer to determine whether a relationship exists between the lunar synodic cycle and human emotional disturbance. A statistically significant lunar periodicity was demonstrated for homicides committed in Dade County, Fla., over a 15-year period. A similar, but nonsignificant, periodicity was found for homicides occurring over a 13-year period in Cuyahoga County, Ohio.
http://ajp.psychiatryonline.org/doi/abs/10.1176/ajp.129.1.69

Lieber A, Sherin C. Homicides and the lunar cycle: toward a theory of lunar influence on human emotional disturbance. Am J Psychiatry 1972;129(1 July):69-74.

https://www.ncbi.nlm.nih.gov/pubmed/641019?dopt=Abstract
11.613 cases, 5 Year Period
Assaults occurred more often around the full moon.

Journal of Psychology, vol. 93:81, 1976.
34.318 cases, 1 year period:
Crimes occurred more frequently during the full moon.

https://www.ncbi.nlm.nih.gov/pubmed/11124173?dopt=Abstract
1.621 cases in 3 year period
Animal bites occured more frequently during the full moon.

Quote
Subjective sleep duration varied with the lunar cycle, from 6 h 41 min at full moon to 7 h 00 min at new moon (P < 0.001).
http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2869.2006.00520.x/full

Quote
Here we show that subjective and objective measures of sleep vary according to lunar phase
http://www.cell.com/current-biology/fulltext/S0960-9822(13)00754-9

Trees and Plants affected by moon adversely:
http://jgp.rupress.org/content/jgp/10/1/41.full.pdf

Historical Evidences
As Shakespeare once warned:
"It is the very error of the moon, She comes more near the earth than she was wont, And makes men mad."

And Hippocrates confirms: "no physician should be entrusted with the treatment of disease who was ignorant of the science of astronomy."

And Pliny the Elder reports that it led to the brain to be 'unnaturally moist' leading to madness.

And, again, we see the truth through Paracelsus
"mania has the following symptoms: frantic behaviour, unreasonableness, constant restlessness and mischievousness. Some patients suffer from it depending on the phases of the moon."

German psychologist Ewald Hering: "with full moon, increasing mania."
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
― Albert Einstein